class_docstr: Represents spans from a bidirectional encoder as a concatenation of two different
  representations of the span endpoints, one for the forward direction of the encoder
  and one from the backward direction. This type of representation encodes some subtlety,
  because when you consider the forward and backward directions separately, the end index
  of the span for the backward direction's representation is actually the start index.
  
  By default, this `SpanExtractor` represents spans as
  `sequence_tensor[inclusive_span_end] - sequence_tensor[exclusive_span_start]`
  meaning that the representation is the difference between the the last word in the span
  and the word `before` the span started. Note that the start and end indices are with
  respect to the direction that the RNN is going in, so for the backward direction, the
  start/end indices are reversed.
  
  Additionally, the width of the spans can be embedded and concatenated on to the
  final combination.
  
  The following other types of representation are supported for both the forward and backward
  directions, assuming that `x = span_start_embeddings` and `y = span_end_embeddings`.
  
  `x`, `y`, `x*y`, `x+y`, `x-y`, `x/y`, where each of those binary operations
  is performed elementwise.  You can list as many combinations as you want, comma separated.
  For example, you might give `x,y,x*y` as the `combination` parameter to this class.
  The computed similarity function would then be `[x; y; x*y]`, which can then be optionally
  concatenated with an embedded representation of the width of the span.
  
  Registered as a `SpanExtractor` with name "bidirectional_endpoint".
  
  # Parameters
  
  input_dim : `int`, required
      The final dimension of the `sequence_tensor`.
  forward_combination : `str`, optional (default = `"y-x"`).
      The method used to combine the `forward_start_embeddings` and `forward_end_embeddings`
      for the forward direction of the bidirectional representation.
      See above for a full description.
  backward_combination : `str`, optional (default = `"x-y"`).
      The method used to combine the `backward_start_embeddings` and `backward_end_embeddings`
      for the backward direction of the bidirectional representation.
      See above for a full description.
  num_width_embeddings : `int`, optional (default = `None`).
      Specifies the number of buckets to use when representing
      span width features.
  span_width_embedding_dim : `int`, optional (default = `None`).
      The embedding size for the span_width features.
  bucket_widths : `bool`, optional (default = `False`).
      Whether to bucket the span widths into log-space buckets. If `False`,
      the raw span widths are used.
  use_sentinels : `bool`, optional (default = `True`).
      If `True`, sentinels are used to represent exclusive span indices for the elements
      in the first and last positions in the sequence (as the exclusive indices for these
      elements are outside of the the sequence boundary). This is not strictly necessary,
      as you may know that your exclusive start and end indices are always within your sequence
      representation, such as if you have appended/prepended <START> and <END> tokens to your
      sequence.
code: def _embed_spans(
      self,
      sequence_tensor: torch.FloatTensor,
      span_indices: torch.LongTensor,
      sequence_mask: torch.BoolTensor = None,
      span_indices_mask: torch.BoolTensor = None,
  ) -> torch.FloatTensor:
      # Both of shape (batch_size, sequence_length, embedding_size / 2)
      forward_sequence, backward_sequence = sequence_tensor.split(
          int(self._input_dim / 2), dim=-1
      )
      forward_sequence = forward_sequence.contiguous()
      backward_sequence = backward_sequence.contiguous()
  
      # shape (batch_size, num_spans)
      span_starts, span_ends = [
          index.squeeze(-1) for index in span_indices.split(1, dim=-1)
      ]
  
      if span_indices_mask is not None:
          span_starts = span_starts * span_indices_mask
          span_ends = span_ends * span_indices_mask
      # We want `exclusive` span starts, so we remove 1 from the forward span starts
      # as the AllenNLP `SpanField` is inclusive.
      # shape (batch_size, num_spans)
      exclusive_span_starts = span_starts - 1
      # shape (batch_size, num_spans, 1)
      start_sentinel_mask = (exclusive_span_starts == -1).unsqueeze(-1)
  
      # We want `exclusive` span ends for the backward direction
      # (so that the `start` of the span in that direction is exlusive), so
      # we add 1 to the span ends as the AllenNLP `SpanField` is inclusive.
      exclusive_span_ends = span_ends + 1
  
      if sequence_mask is not None:
          # shape (batch_size)
          sequence_lengths = util.get_lengths_from_binary_sequence_mask(
              sequence_mask
          )
      else:
          # shape (batch_size), filled with the sequence length size of the sequence_tensor.
          sequence_lengths = torch.ones_like(
              sequence_tensor[:, 0, 0], dtype=torch.long
          ) * sequence_tensor.size(1)
  
      # shape (batch_size, num_spans, 1)
      end_sentinel_mask = (
          exclusive_span_ends >= sequence_lengths.unsqueeze(-1)
      ).unsqueeze(-1)
  
      # As we added 1 to the span_ends to make them exclusive, which might have caused indices
      # equal to the sequence_length to become out of bounds, we multiply by the inverse of the
      # end_sentinel mask to erase these indices (as we will replace them anyway in the block below).
      # The same argument follows for the exclusive span start indices.
      exclusive_span_ends = (
          exclusive_span_ends * ~end_sentinel_mask.squeeze(-1)
      )
      exclusive_span_starts = (
          exclusive_span_starts * ~start_sentinel_mask.squeeze(-1)
      )
  
      # We'll check the indices here at runtime, because it's difficult to debug
      # if this goes wrong and it's tricky to get right.
      if (exclusive_span_starts < 0).any() or (
          exclusive_span_ends > sequence_lengths.unsqueeze(-1)
      ).any():
          raise ValueError(
              f"Adjusted span indices must lie inside the length of the sequence tensor, "
              f"but found: exclusive_span_starts: {exclusive_span_starts}, "
              f"exclusive_span_ends: {exclusive_span_ends} for a sequence tensor with lengths "
              f"{sequence_lengths}."
          )
  
      # Forward Direction: start indices are exclusive. Shape (batch_size, num_spans, input_size / 2)
      forward_start_embeddings = util.batched_index_select(
          forward_sequence, exclusive_span_starts
      )
      # Forward Direction: end indices are inclusive, so we can just use span_ends.
      # Shape (batch_size, num_spans, input_size / 2)
      forward_end_embeddings = util.batched_index_select(
          forward_sequence, span_ends
      )
  
      # Backward Direction: The backward start embeddings use the `forward` end
      # indices, because we are going backwards.
      # Shape (batch_size, num_spans, input_size / 2)
      backward_start_embeddings = util.batched_index_select(
          backward_sequence, exclusive_span_ends
      )
      # Backward Direction: The backward end embeddings use the `forward` start
      # indices, because we are going backwards.
      # Shape (batch_size, num_spans, input_size / 2)
      backward_end_embeddings = util.batched_index_select(
          backward_sequence, span_starts
      )
  
      if self._use_sentinels:
          # If we're using sentinels, we need to replace all the elements which were
          # outside the dimensions of the sequence_tensor with either the start sentinel,
          # or the end sentinel.
          forward_start_embeddings = (
              forward_start_embeddings * ~start_sentinel_mask
              + start_sentinel_mask * self._start_sentinel
          )
          backward_start_embeddings = (
              backward_start_embeddings * ~end_sentinel_mask
              + end_sentinel_mask * self._end_sentinel
          )
  
      # Now we combine the forward and backward spans in the manner specified by the
      # respective combinations and concatenate these representations.
      # Shape (batch_size, num_spans, forward_combination_dim)
      forward_spans = util.combine_tensors(
          self._forward_combination,
          [forward_start_embeddings, forward_end_embeddings],
      )
      # Shape (batch_size, num_spans, backward_combination_dim)
      backward_spans = util.combine_tensors(
          self._backward_combination,
          [backward_start_embeddings, backward_end_embeddings],
      )
      # Shape (batch_size, num_spans, forward_combination_dim + backward_combination_dim)
      span_embeddings = torch.cat([forward_spans, backward_spans], -1)
  
      return span_embeddings
  
file_path: allennlp/allennlp/modules/span_extractors/bidirectional_endpoint_span_extractor.py
imports: import torch
  from torch.nn.parameter import Parameter
  from allennlp.common.checks import ConfigurationError
  from allennlp.modules.span_extractors.span_extractor import SpanExtractor
  from allennlp.modules.span_extractors.span_extractor_with_span_width_embedding import SpanExtractorWithSpanWidthEmbedding
  from allennlp.nn import util
label_desc: Use image node_id 3 for calling the BidirectionalEndpointSpanExtractor obj's underlying member method code with example usage: obj._embed_spans(sequence_tensor, span_indices, sequence_mask, span_indices_mask) and returns: span_embeddings